On the combined performance of nonlocal artificial boundary conditions with the new generation of advanced multigrid flow solvers

We develop theoretically and implement numerically a unified flow solution methodology that combines the advantages relevant to two independent groups of methods in computational fluid dynamics that have recently proven succe ssful: The new factorizable schemes for the equations of hydrodynamics that facilitate the construction of optimally convergent multigrid algorithms, and highly accurate global far-field artificial boundary conditions (ABCs). The primary result that we have obtained is the following. Global ABCs do not hamper the optimal (i.e., unimprovable) multigrid convergence rate pert inent to the solver. At the same time, contrary to the standard local ABCs, the solution accuracy provided by the global ABCs deteriorates very slight ly or does not deteriorate at all when the computational domain shrinks, wh ich clearly translates into substantial savings of computer resources. (C) 2001 Elsevier Science Ltd. All rights reserved.